This study will develop statistical methods for estimating the standardized risk difference and the common odds ratio for a number of contingency tables. The optimality properties of the developed methodology will be investigated and established. The likelihood equations are to be derived. The weighted total, the maximum likelihood and the conditional maximum likelihood methodologies are to be examined. The study has been extended to do comparison of a number of contingency tables in the form of hypothesis testing. All these methodologies have wide applications to epidemiological studies, biomedical studies, genetics and other disciplines. Examples include testing the Hardy- Weinberg Law across strata and comparing the black-white differences in birth weight specific infant mortality curves.